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%I #24 Jul 11 2022 16:05:08
%S 1,2,3,1,5,6,7,1,1,10,11,3,13,14,15,1,17,2,19,5,21,22,23,6,1,26,1,7,
%T 29,30,31,1,33,34,35,1,37,38,39,10,41,42,43,11,5,46,47,3,1,2,51,13,53,
%U 4,55,14,57,58,59,15,61,62,7,1,65,66,67,17,69,70,71,2,73,74,3,19,77,78,79,5
%N a(n) is the smallest positive integer such that a(n)*n = j^k, for some j (j>=1) and k (k>=2).
%H Amiram Eldar, <a href="/A160400/b160400.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A087320(n)/n.
%F a(n) = A007913(n) for n cubefree, a(n) = 1 for n in A001597. - _Charlie Neder_, Dec 26 2018
%p isA001597 := proc(n) local e,p ; if n = 1 then RETURN(true) ; fi; p := [] ; for e in ifactors(n)[2] do p := [op(p), op(2,e) ] ; od: if igcd(op(p)) > 1 then true; else false; fi; end: A160400 := proc(n) local a; for a from 1 do if isA001597(a*n) then RETURN(a) ; fi; od: end: seq(A160400(n),n=1..120) ; # _R. J. Mathar_, May 26 2009
%t a[n_] := SelectFirst[Range[n], GCD @@ FactorInteger[n*#][[;; , 2]] > 1 &]; a[1] = 1; Array[a, 100] (* _Amiram Eldar_, Jul 09 2022 *)
%Y Cf. A087320, A001597, A007913.
%K nonn
%O 1,2
%A _Leroy Quet_, May 12 2009
%E More terms from _R. J. Mathar_, May 26 2009
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